course Mth 163 assignment #011011.
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09:47:05 `questionNumber 110000 `q001. Note that this assignment has 11 questions How many squares one foot on a side would it take to construct a square two feet on a side?
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RESPONSE --> It takes four b/c you need two rows with 2 squares in a row confidence assessment: 3
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09:47:16 `questionNumber 110000 A common response is that it takes 2 one-ft. squares to make a 2-foot square. However, below thought shows that this isn't the case. If we put 2 one foot squares side by side we get a one-foot by two-foot rectangle, not a square. If we put a second such rectangle together with the first, so that we have 2 rows with 2 squares in a row, then we have a two-foot square. Thus we see that it takes 4 squares one foot on a side to make a square 2 ft. on a side.
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RESPONSE --> I understand self critique assessment: 3
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09:47:45 `questionNumber 110000 `q002. How many cubes one foot on a side would it take to construct a cube two feet on a side?
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RESPONSE --> Referring to chpt. 10 notes on sandpile, it takes 8 cubes. confidence assessment: 3
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09:47:55 `questionNumber 110000 We could begin by constructing two rows with two cubes in a row, which would sit on a square two feet by two feet. However this would not give is a cube two feet on a side, because at this point the figure we have constructed is only one foot high. So we have to add a second layer, consisting of two more rows with two cubes a row. Thus we have 2 layers, each containing 2 rows with 2 cubes in a row. Each layer has 4 cubes, so our two layers contain 8 cubes.
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RESPONSE --> I got it. self critique assessment: 3
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09:48:18 `questionNumber 110000 `q003. How many squares one foot on a side would it take to construct a square three feet on a side?
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RESPONSE --> Square 3 ft would take 3 rows with 9 squares. confidence assessment: 2
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09:48:25 `questionNumber 110000 We would require three rows, each with 3 squares, for a total of 9 squares.
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RESPONSE --> i see self critique assessment: 2
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09:48:41 `questionNumber 110000 `q004. How many cubes one foot on a side would take to construct a cube three feet on a side?
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RESPONSE --> It would be 3^3= 27 confidence assessment: 2
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09:48:50 `questionNumber 110000 This would require three layers to make a cube three feet high. Each layer would have to contain 3 rows each with three cubes. Each layer would contain 9 cubes, so the three-layer construction would contain 27 cubes.
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RESPONSE --> I got it. self critique assessment: 2
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09:49:18 `questionNumber 110000 `q005. Suppose one of the Egyptian pyramids had been constructed of cubical stones. Suppose also that this pyramid had a weight of 100 million tons. If a larger pyramid was built as an exact replica, using cubical stones made of the same material but having twice the dimensions of those used in the original pyramid, then what would be the weight of the larger pyramid?
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RESPONSE --> 100 *4=400 *2= 800 million confidence assessment: 2
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09:49:26 `questionNumber 110000 Each stone of the larger pyramid has double the dimensions of each stone of the smaller pyramid. Since it takes 8 smaller cubes to construct a cube with twice the dimensions, each stone of the larger pyramid is equivalent to eight stones of the smaller. Thus the larger pyramid has 8 times the weight of the smaller. Its weight is therefore 8 * 100 million tons = 800 million tons.
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RESPONSE --> I see. self critique assessment: 2
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09:49:48 `questionNumber 110000 `q006. Suppose that we wished to paint the outsides of the two pyramids described in the preceding problem. How many times as much paint would it take to paint the larger pyramid?
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RESPONSE --> There are 4 times the faces to paint, so 4 times the paint. confidence assessment: 2
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09:50:01 `questionNumber 110000 The outside of each pyramid consists of square faces of uniform cubes. Since the cubes of the second pyramid have twice the dimension of the first, their square faces have 4 times the area of the cubes that make up the first. There is therefore 4 times the area to paint, and the second cube would require 4 times the paint
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RESPONSE --> i understand self critique assessment: 2
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09:50:28 `questionNumber 110000 `q007. Suppose that we know that y = k x^2 and that y = 12 when x = 2. What is the value of k?
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RESPONSE --> 12=k(2)^2 12/4=k 3=k confidence assessment: 3
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09:50:42 `questionNumber 110000 To find the value of k we substitute y = 12 and x = 2 into the form y = k x^2. We obtain 12 = k * 2^2, which we simplify to give us 12 = 4 * k. The dividing both sides by 410 reversing the sides we easily obtain k = 3.
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RESPONSE --> I totally understand that. self critique assessment: 3
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09:51:22 `questionNumber 110000 `q008. Substitute the value of k you obtained in the last problem into the form y = k x^2. What equation do you get relating x and y?
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RESPONSE --> y=3x^2 b/c k was 3 confidence assessment: 2
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09:51:33 `questionNumber 110000 We obtained k = 3. Substituting this into the form y = k x^2 we have the equation y = 3 x^2.
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RESPONSE --> I got it. self critique assessment: 3
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09:52:02 `questionNumber 110000 `q009. Using the equation y = 3 x^2, determine the value of y if it is known that x = 5.
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RESPONSE --> y=3(5)^2=y=75 confidence assessment: 2
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09:52:11 `questionNumber 110000 If x = 5, then the equation y = 3 x^2 give us y = 3 (5)^2 = 3 * 25 = 75.
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RESPONSE --> I understand self critique assessment: 2
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09:53:15 `questionNumber 110000 `q010. If it is known that y = k x^3 and that when x = 4, y = 256, then what value of y will correspond to x = 9? To determine your answer, first determine the value of k and substitute this value into y = k x^3 to obtain an equation for y in terms of x. Then substitute the new value of x.
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RESPONSE --> 256=k(4)^3 256/64=k 4=k y=4(9)^3 y=2916 confidence assessment: 2
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09:53:26 `questionNumber 110000 To we first substitute x = 4, y = 256 into the form y = k x^3. We obtain the equation 256 = k * 4^3, or 256 = 64 k. Dividing both sides by 64 we obtain k = 256 / 64 = 4. Substituting k = 4 into the form y = k x^3, we obtain the equation y = 4 x^3. We wish to find the value of y when x = 9. We easily do so by substituting x equal space 9 into our new equation. Our result is y = 4 * 9^3 = 4 * 729 = 2916.
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RESPONSE --> I see. self critique assessment: 2
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09:54:32 `questionNumber 110000 `q011. If it is known that y = k x^-2 and that when x = 5, y = 250, then what value of y will correspond to x = 12?
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RESPONSE --> 250=k(5)^-2= 250/.04=k 6250=k y=6250(12)^-2 y=43.403 confidence assessment: 2
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09:55:05 `questionNumber 110000 Substituting x = 5 and y = 250 into the form y = k x^-2 we obtain 250 = k * 5^-2. Since 5^-2 = 1 / 5^2 = 1/25, this becomes 250 = 1/25 * k, so that k = 250 * 25 = 6250. Thus our form y = k x^-2 becomes y = 6250 x^-2. When x = 12, we therefore have y = 6250 * 12^-2 = 6250 / 12^2 = 6250 / 144 = 42.6, approximately.
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RESPONSE --> Our answers differ but they are close to the same. self critique assessment: 2
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